Limerick may have controlled lengthy periods of the opening half but they created little in front of goal against a home side who were reliant on quick breakaways.
Wexford worked hard and Shane Nolan had a header fly just wide, while in a lightning break out of midfield it was Joey Mulcahy who pulled his shot wide of the right-hand post.
Wexford Youths took a shock 59th-minute lead when Brian Nolan headed home a Dean Broaders corner.
That score ignited Limerick, who were back level four minutes later through Rory Gaffney.
After Mulcahy had missed a great chance for the home side to go back in front, the visitors took the lead on 64 minutes when Jeffrey Judge powered a low shot through a crowded goalmouth and beat keeper Graham Doyle.
Substitute Dom Foley secured the points one minute from the end.
WEXFORD YOUTHS: Doyle, Scallan, Carr, Browne, Corcoran, Brian Nolan, Mulcahy , Molloy (Howe 78), Shane Nolan (Phelan 78), Elmes, Broaders (Furlong 78).
LIMERICK FC: Ryan, Kelly, Purcell, McGrath (Bradley 55), Tracey, Gamble, Judge, Sheahan (O’Brien 63), Gaffney, Behan (Foley 63), Kluciar.
Referee: Adriano Reale (Dublin).